From Homestar Runner to Salad fingers to badgers, stick figure battles, and the End of Ze World, this — dare I call it an artform? — was a cultural touchstone for a generation.
Flash made vector animation available to the masses, and internet distribution of the relatively small video files was a piece of cake. With the filetype now essentially deprecated, the creators gone on to bigger and better things, the distribution sites shut down, it is a dead form. Most of it will be lost forever, although there may be someone archiving some of it for posterity.
A lot of it was lightweight enough that archival sites etc might not have specifically ruled them out, aside from specific efforts to preserve Flash material. There are also modded versions of Flash Player and emulators that can still play SWFs, and FLV remains supported fairly commonly.